My talk consists of two main topics: (i) numerical model evaluation in air quality and (ii) space-time covariance functions on spheres.

(i) We have developed a new method of evaluating numerical models in air quality using monitoring data. For numerical models in air quality, it is important to evaluate the numerical model output in the space-time context and especially to check how the numerical model follows the dynamics of the real process. We suggest that by comparing certain space-time correlations from observations with those from numerical model output, we can achieve this goal. I will demonstrate how our method is applied to a numerical model called CMAQ for sulfate levels over North America.

(ii) For space-time processes on global or large scales, it is critical to use models that respect the Earth's spherical shape. However, there has been almost no research in this regard. We have developed a new class of space-time covariance functions on the sphere crossed with time from a sum of independent processes, where each process is obtained by applying a first-order differential operator to a fully symmetric process on sphere crossed with time. The resulting covariance functions can produce various types of space-time interactions and give different covariance structures along different latitudes. Our approach yields explicit expressions for the covariance functions and can also be applied to other spatial domains such as flat surfaces. I will show the fitted result of our new covariance functions to observed sulfate levels.

Finally, I will describe how we build a space-time model that combines numerical model output and observations to build a space-time map of air pollution levels. The information on space-time covariance structure obtained from numerical model evaluation procedure is useful for building the space-time model. Moreover, the space-time covariance functions on spheres play a critical role here because of large spatial domain.

Refreshments will be served at 3:45 p.m. in Room 008 of the Statistics Building